Extensional Flow Behavior of Methylcellulose Solutions Containing

Feb 27, 2018 - Capillary Breakup Extensional Rheometry (CaBER) was used to characterize salt-free and 8 wt % NaCl solutions of MC at room temperature...
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Letter Cite This: ACS Macro Lett. 2018, 7, 347−352

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Extensional Flow Behavior of Methylcellulose Solutions Containing Fibrils Svetlana Morozova,†,§ Peter W. Schmidt,‡,§ Athena Metaxas,‡,§ Frank S. Bates,‡ Timothy P. Lodge,†,‡ and Cari S. Dutcher*,∥ †

Department of Chemistry, ‡Department of Chemical Engineering and Materials Science, and ∥Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota 55455, United States S Supporting Information *

ABSTRACT: The extensional properties of semidilute aqueous methylcellulose (MC) solutions have been characterized. Pure aqueous MC solutions are shear-thinning liquids at room temperature. With the addition of 8 wt % NaCl, a fraction of MC self-assembles into long fibrils, which modify the rheological properties of the original MC solution. Capillary Breakup Extensional Rheometry (CaBER) was used to characterize salt-free and 8 wt % NaCl solutions of MC at room temperature. The salt-free solutions exhibit only power-law behavior whereas solutions with NaCl exhibit both power-law and elastic regimes. As MC concentration increases, the extensional relaxation time also increases strongly, from 0.04 s at 0.5 wt % to 4 s at 1 wt %. In addition, the apparent extensional viscosity rapidly increases as a function of increasing MC concentration, from 40 Pa·s at 0.5 wt % to 1300 Pa·s at 1 wt %. This behavior is attributed to the presence of fibrils in the MC solutions containing NaCl.

C

While MC has been extensively studied using shear rheology, the extensional flow properties have not been reported for this cellulose derivative, but have been reported for other cellulose ethers, unmodified cellulose, and other polysaccharide solutions.13−16 Recently there has been a renaissance in methods developed for characterizing the extensional properties of polymer melts, polymer solutions, and complex fluids.17−25 Of particular interest to polymer solutions is utilizing capillary-driven thinning to extract a characteristic extensional relaxation time and apparent extensional viscosity.26−29 The Capillary Breakup Extensional Rheometry (CaBER) method provides a rapid, facile method to determine relevant extensional parameters of polymer solutions. Understanding and controlling the viscous and elastic forces in a fluid is crucial for a diverse range of applications that take advantage of free-surface flows. In this Letter, a first study of the influence of fibrils on the extensional flow behavior of MC solutions is presented. One strategy for creating such solutions at room temperature is the use of NaCl. The addition of NaCl has been widely reported to impact the gelation temperature, such that gel temperature decreases monotonically with increasing concentration of NaCl.30−37 The results from CaBER experiments demonstrate that the addition of MC fibrils into MC solutions causes a transition from a

ellulose ethers are a class of cellulose derivatives in which the hydroxyl groups on cellulose are partially substituted with alkoxy groups. These synthetic derivatives are widely used in commercial products as, for example, rheology modifiers. Methylcellulose (MC) is substituted on average with 1.7−2.2 out of 3 hydroxyl groups per anhydroglucose unit.1 At this degree of substitution (DS), the methoxy substituents disrupt the inter- and intramolecular hydrogen bonds that render cellulose insoluble in water. As a result, MC is soluble in water at low temperatures and can be readily used in a variety of food, pharmaceutical, construction, and consumer applications. In addition to aqueous solubility at low temperature, MC reversibly transitions to a turbid hydrogel upon heating. The mechanism of this thermo-reversible process has been debated for decades; however, recent work has demonstrated unequivocally that the gelation transition is concurrent with the formation of long fibrils with a consistent diameter of about 15 nm.2,3 Both linear and nonlinear shear viscoelastic properties have demonstrated that the fibrillar network dictates the mechanical properties of the high temperature gel.4 The MC fibril offers an enticing design component to expand the use of MC in applications not previously considered. Extensional flows are essential in a variety of polymer solution processes, including fiber spinning, printing, porous media flows, extrusion, coating, molding, spraying, film blowing, and more.5−12 Control over the extensional behavior of MC promises to broaden the already impressive range of applications of MC, while simultaneously improving understanding of MC chain and fibril dynamics in aqueous solutions. © XXXX American Chemical Society

Received: January 15, 2018 Accepted: February 22, 2018

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DOI: 10.1021/acsmacrolett.8b00042 ACS Macro Lett. 2018, 7, 347−352

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Figure 1. Rheological evidence of fibril formation. (a) Heating, or the addition of NaCl to MC solutions, leads to fibril formation. We use this to create viscous solutions of MC fibrils embedded within the entangled MC polymer chain solution. (b) Complex modulus magnitude of 1% MC530 as a function of temperature with and without NaCl. The addition of 8 wt % NaCl depresses the gel temperature by 30 °C. (c) G′ and G″ as a function of frequency when annealing the 1 wt MC in 8 wt % NaCl solution at 25 °C for 15 min to 24 h.

shear-thinning power-law fluid behavior to an elastic-like fluid deformation. For rheological studies, aqueous MC solutions were made using an established protocol.2,3,38 MC (DS = 1.8, Mw = 530 kg/mol, Đ = 4.1) was graciously provided by the Dow Chemical Company, and all other reagents were purchased from Sigma-Aldrich and used without further purification. Salt solutions were made by dissolving 8 wt % NaCl along with the desired concentration of MC into Millipore filtered water. These solutions were stored in a freezer at −20 °C and left out at room temperature for 24 h before rheological studies. Further details on the methodology, such as the experimental conditions used for CaBER experiments, can be found in the Supporting Information. The sol−gel transition for aqueous MC solutions has been studied extensively by investigating the shear rheological properties as a function of temperature.38 For salt-free MC solutions, the elastic modulus increases rapidly by several orders of magnitude at ∼60 °C, indicating formation of a fibrillar network (Figure 1b, red curve), as previously confirmed with cryogenic transmission electron microscopy and smallangle scattering.2,3 The addition of NaCl decreases the temperature at which fibrils form and dissolve, and therefore decreases the temperature at which the sol−gel and gel−sol transitions takes place (Figure 1a). To directly compare the sol−gel transition for aqueous MC solutions with and without salt, the complex modulus magnitude |G*| was measured as a function of temperature (Figure 1b). The addition of 8 wt % NaCl leads to an approximately 30 °C decrease in the sol−gel transition temperature, when the MC solutions are heated at 1 °C/min. The gel−sol transition, which is believed to be the lower limit in temperature at which fibril formation can occur,39 is also decreased below room temperature. When annealing 1 wt % MC in 8 wt % NaCl at 25 °C for 24 h, G′ and G″ both increase with time by an order of magnitude (Figure 1c). G′ and G″ still show a distinct dependence on frequency after 24 h, and the solution still flows, as shown with shear viscosity measurements in Figure S1 in the Supporting Information. The increase in both moduli is consistent with the formation of fibrils, near the gelation transition. The consequence of the presence of viscosity-modifying fibrils on the extensional flow behavior is dramatic. Figure 2 shows this comparison: the dark green curve is from a 0.75 wt % MC solution without added salt, whereas the light green curve is for an 0.75 wt % MC solution in 8 wt % NaCl. Fibrils modify the CaBER profile in two ways. The liquid bridge flows

Figure 2. CaBER liquid neck diameter normalized by the plate diameter as a function of time and total MC concentration at 25 °C for 0 and 8 wt % NaCl solutions. The time for liquid bridge breakup increases drastically, and so does the diameter at which we observe elastic extensional behavior characterized by an exponential thinning of the neck diameter. The black lines represent fits to eqs 1 and 2 for each concentration. The measurements were taken with a plate diameter of 4 mm, initial plate separation of 2 mm, final strike height of 8−9 mm, and an exponential strike time of 30−50 ms.

more slowly, and breaks up at later times. More significantly, after the initial shear-thinning power-law behavior, solutions with fibrils now exhibit elastic fluid behavior, as the power-law thinning segues into exponential filament thinning at later times when the polymers or fibrils disentangle and orient.10,26,40−42 Figure 2 also shows CaBER profiles for 0.5, 0.625, 0.875, 125 and 1 wt % MC solutions in 8 wt % NaCl after annealing at room temperature for 24 h. The solutions first flow according to a visco-capillary force balance, for which the nonslender viscous power-law constitutive model for power-law exponents n < 0.6 can be written as24,41,43,44 R mid = A(tc − t )n R0 (1) where Rmid is the liquid bridge midpoint radius, R0 is the plate radius, tc is the critical time to breakup, t is time, n is the powerlaw exponent determined previously from Figure S1, and A is a numerical prefactor. With the presence of fibrils, the visco-capillary balance power law thinning leads into an elasto-capillary force balance, with the liquid bridge thinning with a characteristic extensional relaxation time:45 348

DOI: 10.1021/acsmacrolett.8b00042 ACS Macro Lett. 2018, 7, 347−352

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Figure 3. Summary of fit results. Error bars indicate the range. The errors are most likely due to variations in sample loading. (a) The breakup time from fits to eq 2. (b) Observed Rcrit/R0, the critical diameter at which there is an observed transition from the visco-capillary to the elasto-capillary balance. (c) The relaxation times from fits to eq 3, using an estimated c* = 0.1 wt %. The solid line represents a fit to 0.001 + 1.7· 10−6

⎛ GR ⎞1/3 ⎛ t ⎞ R mid = ⎜ 0 ⎟ exp⎜ − ⎟ ⎝ 2σ ⎠ R0 ⎝ 3λE ⎠ GR 0 1/3 2σ

( )

.

critical radius at this transition can be estimated as R crit ∼ 0.2127

(2)

λEσ 45 . η

For 0.5 wt % MC in 8 wt % NaCl

solutions Rcrit/R0 is 0.03 and increases to 0.18 for 1 wt % MC 8 wt % NaCl solutions (Figure 3b). Beyond Rcrit, the neck diameter decays exponentially with time; this behavior is fit with eq 2. As shown in Figure 3c, the relaxation time, λE, for the decay increases with MC concentration for solutions with NaCl, from 0.04 s for 0.5 wt % MC to 3.9 s for 1 wt %. At the highest MC concentrations, the samples are so viscous that the filament stabilized at a finite diameter. For these samples, a constant to eq 2 was added during the fitting process to accommodate the flow behavior. The relaxation time scales are strongly concentration dependent. The total polymer concentration is above c* ≈ 0.1 wt %,38 and the polymer chains interpenetrate significantly. For our solutions, c > 5c*, and we expect that the chains, especially when heavily strained at the end of the flow, also entangle significantly. Clasen et al.,46 Sachsenheimer et al.47 Arnolds et al.,48 and Liu et al.49 have previously determined that for such cases reptation dynamics dominate the time scales, and that the longest relaxation time depends on the correlation length, a length scale beyond which hydrodynamic interactions are screened. Taking into account the concentration dependence of the correlation length, which is derived in more detail in Supporting Information, the longest relaxation time has a power law dependence on concentration:49−51

where G is the shear modulus, σ is the surface tension, and λE is the extensional relaxation time.

6.3 ± 1.4

( cc* )

is treated as a fitting

constant. The formation of fibrils creates conditions such that elastic and capillary stresses dominate the overall stress balance within the flowing liquid bridge. Elastic forces oppose any capillary stresses and arise from polymer or fibril stretching, orientation, and conformational changes. Figure 3a−c shows the details of the fits for all repeated trials. The tc values from the fits to eq 1 are plotted in Figure 3a. tc marks the critical time at which the flow transitions from a visco-capillary power-law balance to an elasto-capillary balance.26,40,45 As the concentration of MC increases, so does tc, from 0.4 s for 0.5 wt % to 26 s for 1 wt % MC solutions. The

λE ⎛ c ⎞3.4 − 3ν /3ν − 1 ∼⎜ ⎟ λ 0 ⎝ c* ⎠

(3)

where λ0 is the Zimm dynamics relaxation time of a strand between entanglements and ν is the Flory exponent.52 The exponent from the power law fit in Figure 3c is 6.3 ± 1.4, which is consistent with ν = 0.44. The power law exponent is much larger than 3.8, the power law exponent reported previously for cellulose in ionic liquids,14 and which is consistent with ν = 0.5. This may be ascribed to at least two factors. First, the lower Flory exponent is consistent with the poor solvent quality of MC in 8 wt % NaCl solutions. Second, the mixture of fibrils and free MC chains is a complex solution, and it is beyond the scope of this Letter to determine the exact composition (i.e., fibril vs chain) as a function of time and concentration. Despite the complications, the dramatic concentration dependence is consistent with polymer reptation in a highly entangled solution. The apparent extensional viscosity can be calculated from the exponentially thinning region of the profile, using eqs 4−6.45,53

Figure 4. Apparent extensional viscosity, in the exponentially thinning regime, as a function of MC concentration for solutions with 8 wt % NaCl at 25 °C. (a) The apparent extensional viscosity, calculated using eqs 4−6, as a function of Hencky strain for the exponentially thinning region. (b) The average viscosity for all trials in 8 wt % NaCl at Rcrit. The extensional viscosity at the critical strain increases rapidly with concentration. 349

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ACS Macro Letters ηE,app =

σ / R (t ) dϵ(t )/dt

flow. Ec is expected to be close to 1 at the transition between visco-capillary power-law balance and elasto-capillary balance. With increasing concentration Rcrit (Figure 3b) and λE (Figure 3c) increase such that Ec is 1, 4, 0.6, 0.6, and 0.6 for 0.5 wt % to 1 wt % MC solutions in 8 wt % NaCl, respectively. The value is order unity as expected, with differences from unity within the error of the measurements. For MC solutions without salt, only shear thinning profiles are observed because of the low Deborah numbers 3 1/2 (De = λEσ 1/2/(ρR crit ) ) of the flows at Rcrit, for a solution of density ρ. De is a value that compares the elastic stress relaxation time scales to the Rayleigh time scale for inertiacapillary breakup of a fluid jet.10,55 For all 8 wt % NaCl MC solutions, De > 1, and is equal to 26 for 0.5 wt % MC, 80 for 0.625 wt % MC, 121 for 0.75 wt % MC, 100 for 0.875 wt % MC, and 155 for 1 wt % MC in 8 wt % NaCl. Without salt, the largest possible estimated De for a 1 wt % MC solution is ∼7 and decreases steadily for lower concentrations, using values for λZimm and hypothetical Rcrit estimated in the Supporting Information. For low De, characteristic flow times are much shorter and generalized Newtonian-like breakup dynamics are observed. As shown in Figure 5a, the flow shows a “cusp-like” profile. Self-association of MC into fibrils controls the extensional flow properties of MC solutions in several key ways. Without fibrils, the Deborah number of MC solutions is too low and fluid flow times are much faster than polymer relaxation times. Consequently, 0.5−1 wt % MC solutions with no salt show a power-law “cusp-like” CaBER profile as shown in Figure 5a. The addition of NaCl to the MC solutions to form fibrils increases the relaxation times, viscosity, and Rcrit of the solution such that elasto-capillary regime becomes accessible and experimentally tunable. The distinct thin filament shown in Figure 5b is characteristic for elasto-capillary thinning behavior of elastic fluids. Varying the MC and salt concentrations accesses a regime of stable extensional flows, which have never before been characterized for aqueous MC solutions. These flows open the already commercially relevant polymer to a myriad of other processes, such as fiber spinning and extrusion.

(4)

where the Hencky strain is ⎛R ⎞ ϵ = 2 ln⎜ 0 ⎟ ⎝R⎠

(5)

and the strain rate, dε(t)/dt, is defined as dR mid(t ) dϵ(t ) 2 2 =− = dt R mid(t ) dt 3λE

(6)

The surface tension of the 8 wt % NaCl MC solutions was estimated using a semiempirical model developed by Dutcher et al.54 At a temperature of 25 °C, the surface tension was calculated as 74.4 mN/m. Using the determined value for λE, and the calculated value for the surface tension due to the presence of 8 wt % NaCl, the apparent extensional viscosities are determined for all five concentrations and the values plotted as a function of Hencky strain in Figure 4a. The apparent extensional viscosity increases drastically with concentration, from 40 Pa s for 0.5 wt % MC to 1300 Pa·s for 1 wt % MC as shown in Figure 4b. As the liquid bridge thins, the apparent extensional viscosity increases linearly with the Hencky strain, indicating a constant extension rate, as expected from eq 6. Figure 5 summarizes the important findings: while salt-free MC solutions at room temperature are strongly shear-thinning,

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsmacrolett.8b00042. Detailed Materials and Methods, Figure S1, and derivations of eq 4 (PDF).

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λEσ ηR crit

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

the addition of fibrils increases the viscosity drastically such that elasto-capillary filament thinning is observed starting at 0.5 wt % MC. This difference can be quantified by the elastocapillary number:10,45 Ec =

ASSOCIATED CONTENT

S Supporting Information *

Figure 5. Schematic and experimental snapshots of 0.75 wt % MC behavior as a result of applied extensional flow from the CaBER. (a) In the case of salt-free MC solutions, the power law fluid profiles indicate only free MC chains were present. (b) In the case of MC solutions with 8 wt % NaCl, elastic behavior was observed because MC fibrils are present in addition to free MC chains. For these images, the initial height between the plates was 2 mm, the final height was 13 mm, and the exponential strike time was 30 ms to capture the disparate behavior between MC solutions with and without salt. The images were extracted from videos recorded at 120 fps. The fluid between the top and bottom plates was false colored with black to more clearly depict the filament.

Frank S. Bates: 0000-0003-3977-1278 Timothy P. Lodge: 0000-0001-5916-8834 Cari S. Dutcher: 0000-0003-4325-9197 Author Contributions §

These authors contributed equally to this work (S.M., P.W.S., and A.M.).

(7)

Notes

which compares the time scales of elastically controlled thinning with the viscous time scales that drive the capillary

The authors declare no competing financial interest. 350

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ACKNOWLEDGMENTS This work was supported primarily by the National Science Foundation through the University of Minnesota MRSEC under Award Number DMR-1420013. A.M. was supported through a National Science Foundation Graduate Research Fellowship.

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DOI: 10.1021/acsmacrolett.8b00042 ACS Macro Lett. 2018, 7, 347−352